So far, we have studied the stochastic thermodynamics of FBM-driven systems by introducing and exploiting different definitions of temperatures, medium entropy productions and heat functions. These definitions were motivated by
the desire to formulate, consistent with standard ST for Brownian motion,
an IFR based on path probability ratios involving the total entropy production.
We have shown that in order to achieve such as consistency, one has to introduce either a time-nonlocal temperature \(T(t_1-t_2)\) , or a generalized heat function \(\mathbb {Q}\) . Both quantities seem rather artificial.
In the following section, we will shed some light on these quantities by utilizing a perturbation method [1]}, [2]}, [3]}, [4]}, [5]}.
